The government has abandoned plans to grant pre-charge anonymity to men accused of rape after an outcry from Labour and women Tory MPs.

Crispin Blunt, the justice minister, has said the government will instead negotiate with the Press Complaints Commission to persuade newspapers and websites to grant anonymity to suspects.

The decision marks a change of heart by the coalition, which had pledged to act on the issue. The coalition agreement stated: "We will extend anonymity in rape cases to defendants."

Blunt outlined the new thinking to MPs last week. He said MPs on all sides had agreed in 2003, during the passage of the Sexual Offences Act, that all suspects should have their identity protected from the point of arrest until they are charged. He said the PCC's guidance, issued in 2004, was not strong enough, but the answer was not to introduce fresh legislation.

"We want in the first instance to try to find a non-statutory solution," Blunt told MPs last Tuesday. "Given that we had 21 criminal justice acts passed over the 13 years of the last administration, I am sure that Labour [MPs] will understand why we are loth to find even more statutes to put on the statute book."

The pledge marks something of a U-turn by the coalition. Blunt told MPs on 8 July: "The government are minded to strengthen anonymity up to the point of charge."

His plan was criticised by Labour as "deeply disturbing". Harriet Harman said it could reduce the number of convictions for rape by sending out a signal that women are not to be believed.

Louise Bagshawe, the novelist and Conservative MP for Corby, said: "Singling out rape in this way, ministers are sending a negative signal about women and those who accuse men of rape."

Yvette Cooper, the shadow minister for women and equalities, said the government's proposal was a retrograde step. "The government is pushing ahead with these controversial plans which could prove so damaging for rape convictions without any formal consultation.

"The government has failed to give any reason why rape should be treated differently to any other crime – and chose, instead, to send out the very strong signal that women are not to be believed."

There was some surprise when the Tories and the Lib Dems included the proposal in their coalition agreement. It was not included in either party's manifesto.

Defendants lost the right to anonymity in 1988. Reporting restrictions for both the claimant and defendant in a rape case had been introduced in the 1976 Sexual Offences (Amendments) Act.

It is estimated that 9% of rape allegations are false, the same rate as for other type of crime. Advocates of anonymity have called for reforms to protect those found not guilty, because half of cases brought to court lead to conviction. Government sources said Blunt had not performed a U-turn because ministers had not committed themselves to changing the law. Ministers are still committed to granting anonymity to suspects between arrest and charge and believe that a change in the PCC code is the best way of achieving this.